This invention is in the field of seismic prospecting for oil and gas reserves, and is more specifically directed to such prospecting utilizing amplitude-versus-offset analysis in seismic surveys.
The use of seismic surveys in the search for oil and gas reservoirs is commonplace. As is rudimentary in the art, seismic surveys are performed by imparting acoustic energy of a known amplitude and frequency pattern at one or more locations of the earth (either at a land surface or in a marine environment), and then detecting reflected and refracted acoustic energy at other locations. The delay time between the imparting of the acoustic energy at the source location and detection of the same wave at a receiver location is indicative of the depth at which a particular reflecting geological interface is located. The field of seismic data analysis is concerned with techniques for analyzing the detected acoustic energy to determine both the location and also the properties of various geological strata.
A known technique in the generation and analysis of conventional seismic surveys is referred to as amplitude-versus-offset ("AVO") analysis. According to the AVO approach, attributes of a subsurface interface are determined both from the normal-incidence amplitude of reflected seismic energy and also from the dependence of the detected seismic reflections on the angle of incidence of the energy. According to conventional AVO analysis, multiple seismic traces (i.e., time-domain signals at different detection locations) that include a signal from a common reflection point are collected into a common-depth point (CDP) gather. Typically, a series of common reflection points for the same source-receiver pairs underlie the same surface location at the midpoint between the source and receiver for multiple offsets; as such, this gather is also often referred to as a common midpoint (SAP) gather. The amplitude R of a reflected seismic wave from an interface (i.e., the "target horizon"), as a function of the angle of incidence .theta. from the normal, varies within a CMP gather according to the following relationship: EQU R(.theta.)=A+Bsin.sup.2 .theta.
In this case, the coefficient A is the zero-offset response (also referred to as the AVO intercept), while the coefficient B is referred to as the AVO slope, or gradient, as it is representative of the rate of change of amplitude with the square of the angle of incidence.
For a given reflection event from a horizon between two geological formations, the values of A and B will depend upon the physical properties of the two formations. The well-known Zoeppritz equations provide closed form equations for the response R(.theta.) based upon the compressional velocities (V.sub.P), shear velocities (V.sub.S), and densities (.rho.) of the two formations at the reflecting interface. However, inversion of the Zoeppritz equations to solve for the elastic properties of the formations from reflection data is impractical, due to numerical complexity.
By way of further background, the calculation of theoretical values for A and B for isolated rock interfaces (i.e., at specific horizons) through the use of the linearized Zoeppritz equations and based upon typical values for compressional velocity, density and Poisson's ratio for the strata on either side of the interface of interest, is described in Swan, "Properties of direct AVO hydrocarbon indicators", Offset-dependent reflectivity--Theory and Practice of AVO analysis (Castagna, J. P. & Backus, M. M., eds., Soc. Expl. Geophys., 1993), pp. 78-92. As described therein, variations in the A and B values for particular interfaces from a theoretical A-versus-B trend line for the expected stratigraphic sequences can indicate the location of interfaces in the survey. These variations have resulted in the generation of various "indicators" by way of which anomalous points in the AVO survey (anomalous relative to the background AVO behavior) may be identified. Depending upon the indicator, the anomalous AVO points can be used to specifically identify hydrocarbon-bearing formations in the earth. Examples of AVO seismic survey methods that are based upon the generation of AVO indicators are described in U.S. Pat. No. 5,661,697, and in copending applications Ser. No. 08/614,744, filed Mar. 13, 1996 and Ser. No. 08/654,258, filed May 28, 1996, all of which are commonly assigned herewith and incorporated hereinto by this reference.
However, it has been observed that certain variations in the portion of the earth being surveyed can contaminate the AVO analysis, by inserting offset-dependent variations in the seismic energy that are not due to the presence (or absence) of hydrocarbons. For example, overburden layers have been observed to cause variations in the AVO information. Accordingly, as described in U.S. Pat. No. 5,515,335, commonly assigned herewith and incorporated herein by this reference, it is desirable to modify the AVO behavior of the background points (i.e., points in the AVO traces that are not anomalous, in the surveying sense) so as to eliminate contamination from these offset-dependent effects. This approach measures the standard deviations and correlation coefficient of the AVO intercept (A) and AVO slope (B) within windows (varying in time and CMP location), and then adjusts the AVO intercept (A) and AVO slope (B) values within this window so that the adjusted AVO traces have standard deviations and correlation matching a "desired" set of statistics. According to this approach, the "background" behavior of the AVO data over the survey region is made uniform, and is thus independent of overburden effects and other offset-dependent contamination.
While the method of correcting for overburden described in the above-incorporated U.S. Pat. No. 5,515,335 is useful in many surveys, it has been observed, in connection with the present invention, that this correction approach has limitations, particularly in certain geological formations. As noted above, the overburden correction process is intended to adjust the AVO data only for the background data, and ought not affect the anomalous AVO points, which are interesting from a prospecting standpoint due to their different AVO intercept (A) and AVO slope (B) values (or indicator values) from the background. Indeed, it has been observed, in connection with the present invention, that application of the overburden correction of U.S. Pat. No. 5,515,335 has modified the AVO intercept (A) and AVO slope (B) values for the anomalous points in such a way as to render these points less indicative in the prospecting sense. In some cases, as will now be described relative to FIGS. 1a and 1b, the overburden correction has modified the anomalous points to such an extent as to change their classification.
FIG. 1a illustrates an AVO plot of points within a sizable window of seismic signal data in a survey. In this example, a window of seismic traces covering 200 CMPs and 700 msec in time was analyzed according to conventional methods so that each sample point in the window was assigned an AVO intercept (A) value and an AVO slope (B) value. FIG. 1a is a cross-plot of the AVO intercept (A) and AVO slope (B) values for these points in the window, after normalization of the AVO slope (B) values to have substantially the same statistical range as the AVO intercept (A) values; this normalization does not affect the correlation or other statistics used in the modification for elimination of overburden effects.
In FIG. 1a, the background distribution of AVO intercept (A) and AVO slope (B) values is evident near the origin of the cross-plot, and indicated by the intense distribution thereat (i.e., the white region). This background tends to have a negative correlation between the AVO intercept (A) and AVO slope (B) values, as evident from the slope of the distribution extending into the second and fourth quadrants (QII, QIV, respectively) of the cross-plot. In contrast, certain anomalous points are also evident in the cross-plot of FIG. 1a. These anomalous points tend to have a positive correlation between the AVO intercept (A) and AVO slope (B) values. Examples of specific anomalous points illustrated in FIG. 1a include point C3 in quadrant QIII, which corresponds to a Class III anomaly, and point C4 along the negative A axis, which corresponds to a Class IV anomaly. As is known in the art, a Class III AVO anomaly such as point C3 (i.e., an outlying point in quadrant QIII) indicates the possible presence of a low impedance gas sand below a low impedance shale, while a Class IV AVO anomaly such as point C4 (i.e., an outlying point near the negative A axis) indicates the possible presence of a low impedance gas sand below a high impedance shale. Further background regarding the classification of AVO anomalies is provided in Castagna and Swan, "Principles of AVO crossplotting", The Leading Edge (April, 1997), pp. 337-342; and in Castagna, Swan, and Foster, "Framework for AVO gradient and intercept interpretation", Geophysics, Vol. 63, No. 3 (May-June, 1998), pp. 948-956, both incorporated hereinto by this reference. Anomalies such as points C3, C4 are thus interesting from a seismic prospecting standpoint, because their AVO characteristics are indicative of certain geological formations that relate to hydrocarbon reserves.
As discussed above, however, modification of the AVO intercept (A) and AVO slope (B) values or traces in an AVO survey is useful to eliminate offset-dependent signal contamination such as those due to overburden effects. As described in U.S. Pat. No. 5,515,335, a known technique for eliminating such effects matches the correlation coefficients between the AVO intercept (A) and AVO slope (B) values over multiple windows in the seismic survey, such that the background statistics (against which possible anomalous points are measured) are uniform over the seismic section. If these background statistics are not made uniform, the identification of important anomalous points becomes difficult, as a point may have a significant hydrocarbon indicator (i.e., indicative of an important feature) in one portion of the seismic section, but may become part of the background in another portion of the seismic section. In other words, uniformity in the background statistics over the seismic section allows important anomalies to be identified in each portion of the seismic section, without generating a large number of false positives in any portion of the section (e.g., portions having a low correlation between the AVO intercept (A) and AVO slope (B) values).
Conventional techniques for matching the background statistics over the section, such techniques as described in U.S. Pat. No. 5,515,335, utilize the so-called L2 statistics to modify the AVO intercept (A) and AVO slope (B) traces in the survey. An example of the determination and use of the L2 statistics for a group of points in A-B space is described in the above-incorporated U.S. Pat. No. 5,515,335. According to this approach, a digital computer determines the amplitude standard deviations .sigma..sub.a, .sigma..sub.b, and also the correlation coefficient r of the AVO intercept (A) and AVO slope (B) values of A and B for each depth point in the window under analysis. These calculations are preferably made using complex, or analytical, traces A.sub.c (t), B.sub.c (t) for each surface location, generated as the sum of real traces for the A and B values over time (i.e., A(t), B(t), respectively) and the square root of -1 times their respective Hilbert transform. The standard deviations .sigma..sub.a, .sigma..sub.b are estimated according to the following equations: ##EQU1## where the index i refers to the i.sup.th depth point within window W.sub.i, where .vertline.A.sub.c (i).vertline. and .vertline.B.sub.c (i).vertline. are the magnitudes of the analytical trace coefficients at the i.sup.th depth point, and where n is the number of depth points i in each trace. If desired, a weighted averaging method may be used in the generation of these statistics, for example with the weighting decreasing toward zero at the edges of the window. The digital computer also determines a correlation coefficient r according to the following relationship: ##EQU2## where B.sub.c *(i) is the value of the complex conjugate of the AVO slope B.sub.c at the i.sup.th depth point. Once these statistics are derived for the points within the current window, the digital computer may then determine whether the statistics are sufficiently well-behaved as to produce an accurate result; if not, the size of the analysis window may be adjusted.
As described in the above-incorporated U.S. Pat. No. 5,515,335, desired statistics .sigma..sub.a.sup.d, .sigma..sub.b.sup.d and r.sub.d are selected based upon intuitive assumptions, or upon previous analysis of the portion of the earth being surveyed. The AVO intercept (A) and AVO slope (B) traces are then modified, based on these desired statistics, to render the background statistics uniform over the survey section. For example, modified AVO intercept traces A.sub.m (t) and modified AVO slope traces B.sub.m (t) may be generated as follows: ##EQU3## Typically, the desired standard deviations .sigma..sub.a.sup.d, .sigma..sub.b.sup.d are simply equated to the estimated standard deviations .sigma..sub.a, .sigma..sub.b, in which case A.sub.m (t) simply equals the original analytical trace A.sub.c (t). However, the modified AVO slope trace B.sub.m (t) is both scaled and translated, according to the corresponding AVO intercept values A.sub.c (t), as well as the desired and actual statistics.
However, it has been observed, in connection with the present invention, that this operation of matching of the statistics of the seismic section windows to the desired statistics can change the AVO intercept (A) and AVO slope (B) values of anomalous points to such an extent that their character as outliers can change. FIG. 1b is a cross-plot of the points of FIG. 1a, after modification of the traces in the manner described above, to correspond to a desired correlation coefficient r.sub.d of -0.6. As evident from FIG. 1b, the background distribution of points (indicated by the high intensity region of the cross-plot near the origin) has narrowed and become more elongated, indicative of a more negative correlation coefficient. However, anomalous point C3 has moved toward the negative A axis, so as to now resemble a Class IV anomaly, rather than its true character as a Class III anomaly. Indeed, comparison of FIGS. 1a and 1b indicates that the quadrant QIII outliers of FIG. 1a have moved toward the background, with some moving into quadrant QIV. Additionally, Class IV anomaly point C4 of FIG. 1a has moved fully into quadrant QII of FIG. 1b as a result of the modification process, and is approaching the background trend. Accordingly, the process of modifying the AVO intercept (A) and AVO slope (B) traces to the desired correlation statistics, for purposes of eliminating contamination due to overburden and the like, has the undesired effect of moving anomalous points into the background. As a result, the conventional overburden correction process reduces the sensitivity of conventional AVO analysis in detecting true anomalous points that may be indicative of hydrocarbon-bearing formations.
By way of further background, techniques for the generation of statistics for each distribution within a population of jointly distributed variables, such as jointly Gaussian distributions, are known in the art. An example of such a technique is present within the MATHEMATICA 3.0 computer program, available from Wolfram Research.